Oil Quality and Price
Quality of Oil Is Measured in API

Oil Quality and Price
Quality of oil is measured in API gravity degrees--the higher the degrees API,the higher the quality.The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel.
$$\begin{array} { | c | c | } \hline \text { Oi degrees API } & \text { Price per barrel (in \$) } \\\hline 27.0 & 12.02 \\28.5 & 12.04 \\30.8 & 12.32 \\31.3 & 12.27 \\31.9 & 12.49 \\34.5 & 12.70 \\34.0 & 12.80 \\34.7 & 13.00 \\37.0 & 13.00 \\41.0 & 13.17 \\41.0 & 13.19 \\38.8 & 13.22 \\39.3 & 13.27 \\\hline\end{array}$$ A partial Minitab output follows:
$$\begin{array}{l}\text { Dascriptive atafistics }\\\begin{array} { l l l l l } \text { Variable } & \mathrm { N } & \text { Mear } & \text { StDev } & \text { SE Mear } \\\text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \\\text { Price } & 13 & 1270 & 0.757 & 0.127\end{array}\end{array}$$ $$\begin{array}{l}\begin{array} { l l } \text { Covariances }&&\\&\text { Degeres } & \text { Price } \\\text { Degeres } &21.281667 & \\\text { Price } &2.026750 & 0.208933\end{array}\end{array}$$ $$\begin{array}{l}\text { Analysis of Variance }\\\begin{array} { l l r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text {p}\\\text { Regeression } & 1 & 2.3162 & 2.3162 & 134.24&0.000 \\\text { Resichul Entar } & 11 & 0.1898 & 0.0173 & \\\text { Total } & 12 & 2.5060 & &\end{array}\end{array}$$
-In a simple linear regression model,testing whether the slope $\beta$ ₁ of the population regression line could be zero is the same as testing whether or not the population coefficient of correlation $\rho$ equals zero.